vertexEdgeMatrix -- computes the vertex-edge-relations matrix

Synopsis

• Usage:

  M = vertexEdgeMatrix P

• Inputs:
  • P, a convex polyhedron
• Outputs:
  • M, a matrix

Description

vertexEdgeMatrix computes the matrix M where the columns are indexed by the edges and the rows are indexed by the vertices of P and has 1 as an entry if the corresponding edge contains this vertex and 0 otherwise.

i1 : P = cyclicPolytope(3,5)

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 6
      number of rays => 0
      number of vertices => 5

o1 : Polyhedron

i2 : vertexEdgeMatrix P

o2 = | 0 1 2 3 4 5 6 7 8 9 |
     | 1 1 0 1 1 0 0 1 0 0 |
     | 2 0 1 1 0 0 0 0 0 1 |
     | 3 1 1 0 0 1 0 0 1 0 |
     | 4 0 0 0 1 1 1 0 0 0 |
     | 5 0 0 0 0 0 1 1 1 1 |

              6        10
o2 : Matrix ZZ  <--- ZZ